1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basis R 2

  1. Feb 28, 2010 #1
    x1= column vector (2, 1)
    x2= column vector (4, 3)
    x3= column vector (7, -3)

    Why must x1, x2, and x3 be linearly dependent?

    x1 and x2 span R^2.
    The basis are these two columns vectors: (3/2, -1/2), (-2, 1)

    Since x1 and x2 form the basis, x3 can be written as a linear combination of these vectors.

    Is that it? or correct?
     
  2. jcsd
  3. Feb 28, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    How to answer that question depends on what you have learned. What is the dimension of R2?
    There is no such thing as the basis for R2. Any two linearly independent vectors in R2 are a basis.
    You could just demonstrate x3 = cx1 + dx2; that would surely settle it.
     
  4. Feb 28, 2010 #3
    New question:
    x1=(3, -2, 4)
    x2=(3, -1, 4)
    x3=(-6, 4, -8)

    What is the dimension of span (x1, x2, and x3)

    The book says 1; however, shouldn't the dimension be 3? I see that these 3 vectors are all the same times a constant but there are coordinates.
     
  5. Feb 28, 2010 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If they are supposed to be a constant times each other you have mistyped something. But assuming that, what is the definition of dimension that you are using? You have to apply that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Basis R 2
  1. Basis R 2 (Replies: 7)

  2. Vector Basis of R^n (Replies: 0)

Loading...